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# Computational Mathematics

### Presentation

Introduction, foundation and study of numerical methods and concepts used in the numerical resolution of the most relevant mathematical problems in engineering. Error estimation and convergence and stability analysis of the numerical method.

### Programme

Science in Aerospace Engineering

| Semestral | 5

### Year | Type of course unit | Language

2 |Mandatory |Português

ULP1393-3561

### Recommended complementary curricular units

Algorithms and Programming

Calculus I

Calculus II

Não

### Syllabus

1. Computational Arithmetic

• Representation of numbers;
• Rounding;
• Errors and error propagation;

2. Nonlinear Equations

• Bisection method;
• Secant method;
• Newton's method;
• Fixed-point method;

3. Polynomial interpolation

4. Numerical Derivation and Integration

5. Systems of linear and non-linear equations

• Linear Equation Systems
• Nonlinear Equation Systems

6. Numerical solution of differential equations

• Single Step Methods:
• Multistep methods (multiple-step);

### Objectives

Understand the fundamentals of the studied numerical methods as well as their framing in the context of engineering. Know how to apply these methods using computer applications. Additionally, present students with the use of specific software (Octave) to solve computational mathematical problems.

### Teaching methodologies and assessment

Classes are theoretical and practical, where the theoretical exposition of the syllabus is accompanied by the presentation of practical examples and the resolution of exercises. Individual and autonomous study outside the classroom environment is encouraged and considered fundamental. Some time will also be dedicated to preparing the computational project that will be part of the evaluation.

The course website on the Moodle platform will be used to present the syllabus and pedagogical support materials, as well as the delivery of work by the students.

According to the ULP Assessment Regulation, the student will choose the assessment regime: continuous (mixed type) or final.

Continuous:

• Practical assignment - 30%
• Final Exam 70%

(Minimum grade in each element - 8/20)

Final:

• Final Exam - 100%

### References

• Pina, Heitor - Métodos Numéricos. 1ª Edição, Escolar Editora, 2010, 888 p., ISBN: 978-972-592-284-2
• Valença, Maria Raquel - Análise Numérica. 1ª Edição, Universidade Aberta, 1996, 318 p., ISBN: 972-674-195-5

### Office Hours

A combinar entre o docente e os alunos.